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In our empirical study we examine the dynamics of the price evolution of liquid stocks after experiencing a large intra-day price change, using data from the NYSE and the NASDAQ. We find a significant reversal for both intra-day price decreases and increases. Volatility, volume and, in the case of the NYSE, the bid-ask spread, which increase sharpl...

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... For instance, it has been shown that spread has a distribution that is fat-tailed and its dynamics is characterized by a long range (power-law) auto-correlation function [33,36,8,9,26,18]. In refs [33,37,44], it is shown that after a large variation of the spread (i.e., a temporary liquidity crisis), the spread decays slowly back to an equilibrium value. Let us note that, though, most of the time, these statistical properties are obtained through direct empirical studies on historical spread time-series, some papers tackle the statistical properties of the spread (mainly the distribution of the spread values) via some statistical models of the limit and market order flows [22,14,40,10,39,1]. ...
Preprint
The bid-ask spread, which is defined by the difference between the best selling price and the best buying price in a Limit Order Book at a given time, is a crucial factor in the analysis of financial securities. In this study, we propose a "State-dependent Spread Hawkes model" (SDSH) that accounts for various spread jump sizes and incorporates the impact of the current spread state on its intensity functions. We apply this model to the high-frequency data from the Cac40 Euronext market and capture several statistical properties, such as the spread distributions, inter-event time distributions, and spread autocorrelation functions.
... directly introduce the power law model to capture the decaying patterns of volatility after extreme events [5,8,9,12] . [6,7] introduce the Multifractal random walk (MRW) model [13] , which unifies the properties of volatility multi-fractality and long-range dependence. ...
... From, one can see that the decays of volatility are close to power laws at later times, which is consistent with previous studies [5,8,9] , and one can also see that the volatility decays deviate from the power laws in the initial stage of the decays. These results indicate that the evolution behavior of volatility may differ in different stages after extreme events. ...
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... Numerous other papers have subsequently confirmed these findings (see, Amini et al., 2013; for a review of this literature). Many different markets have been studied including individual stocks (Zawadowski, Andor, and Kertész, 2006;Lobe and Rieks, 2011), stock market indices (Rezvanian, Turk, and Mehdian, 2011;Yu, Rentzler, and Tandon, 2010), futures markets (Fung, Mok, and Lam, 2000;Grant, Wolf, and Yu, 2005), government bonds (Kassimatis, Spyrou, and Galariotis, 2008), commodity futures (Mazouz and Wang, 2014) and cryptocurrency markets (Borgards and Czudaj, 2020). The precise methodology used in this literature varies across papers as do some of the empirical findings. ...
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... For instance, Nam, Pyun, and Avard [2], Cox and Peterson [3] and Atkins and Dyl [4] investigate short-term price reversals, ranging over time periods from a few days up to a month, and find that they occur following a 1-day extreme price movement. Zawadowski, Andor and Kertesz [5] and Grant, Wolf and Yu [6] find significant intraday price reversals following a large intraday price change. Kudryavtsev [7] finds that the stock price reversals during subsequent trading days follow relatively large price moves towards the end of the trading days. ...
... The value of the exponent θ seems to depend on the nature of the initial price jump. When the jump occurs because of an exogenous news, θ ≈ 1 [Lillo 2003, Joulin 2008, whereas when the jump appears to be of endogenous origin, the value of θ falls around θ ≈ 1 2 [Zawadowski 2006, Joulin 2008. In other words, as noted in [Joulin 2008], the volatility seems to resume its normal course faster after a news than when the jump seems to come from nowhere. ...
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... Interestingly, the average volatility is found to decay in the first two hours of trading as a power-law k −β with β ≈ 0.3. This relaxation is reminiscent of the power-law decay of the volatility after large price swings [11, 16, 18, 10]. The overnight return is indeed usually quite large, and can be seen as a strong perturbation. ...
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We establish several new stylised facts concerning the intra-day seasonalities of stock dynamics. Beyond the well known U-shaped pattern of the volatility, we find that the average correlation between stocks increases throughout the day, leading to a smaller relative dispersion between stocks. Somewhat paradoxically, the kurtosis (a measure of volatility surprises) reaches a minimum at the open of the market, when the volatility is at its peak. We confirm that the dispersion kurtosis is a markedly decreasing function of the index return. This means that during large market swings, the idiosyncratic component of the stock dynamics becomes sub-dominant. In a nutshell, early hours of trading are dominated by idiosyncratic or sector specific effects with little surprises, whereas the influence of the market factor increases throughout the day, and surprises become more frequent.
... Each player tries to do this as slowly as possible in order to get a more favorable price from the incoming market orders, but at the same time competition prevents this from being too slow. Empirically this slow decay has been measured in Zawadowski et al. [2006], Ponzi et al. [2008]. One way of quantifying the average dynamics is by computing the quantity, Ponzi et al. [2008], ...
... The decay of G(τ |∆) as a function of τ is very slow and for large values of τ is compatible with a power law decay with a fitted exponent in the range 0.4 − 0.5. A similar slow decay of the volatility after a shock has been reported in Lillo and Mantegna [2003], Zawadowski et al. [2006], Joulin et al. [2008]. ...
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... The volatility pattern in the case of news is much wider than the rather narrow peak corresponding to endogenous jumps. In both cases, we find (Figure 5) that the relaxation of the excess-volatility follows a power-law in time σ(t) − σ(∞) ∝ t −β (see also [22] [23]). The exponent of the decay is, however, markedly different in the two cases: for news jumps, we find β ≈ 1, whereas for endogenous jumps one has β ≈ 1/2. ...
... The exponent of the decay is, however, markedly different in the two cases: for news jumps, we find β ≈ 1, whereas for endogenous jumps one has β ≈ 1/2. Our results are compatible with those of [22], who find β ≈ 0.35. The difference between endogenous and endogenous volatility relaxation has also been noted in [17], but on a very restricted set of news events. ...
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In order to understand the origin of stock price jumps, we cross-correlate high-frequency time series of stock returns with different news feeds. We find that neither idiosyncratic news nor market wide news can explain the frequency and amplitude of price jumps. We find that the volatility patterns around jumps and around news are quite different: jumps are followed by increased volatility, whereas news tend on average to be followed by lower volatility levels. The shape of the volatility relaxation is also markedly different in the two cases. Finally, we provide direct evidence that large transaction volumes are_not_ responsible for large price jumps. We conjecture that most price jumps are induced by order flow fluctuations close to the point of vanishing liquidity.
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Diffusion of defaults among financial institutions by G. Demange.- Systemic risk and complex systems: a graph-theory analysis by D. Lautier, F. Raynaud.- Omori Law after Exogenous on Supplier-Customer Network by Y. Fujiwara.- Aftershock prediction for high-frequency financial markets' dynamics by F. Baldovin, F. Camana, M. Caraglio, A.L. Stella, M. Zamparo.- How unstable are complex financial systems ? Analyzing an inter-bank network of credit relations by S. Sinha, M. Thess, S. Markose.- Study of statistical correlations in intraday and daily financial return time series by G. Tilak, T. Szell, R. Chicheportiche, A. Chakraborti.- A robust measure of investor contrarian behaviour by D. Challet, D. Morton de Lachapelle.- Evolution of Zipf's Law for Indian Urban Agglomerations vis-a-vis Chinese Urban Agglomerations by K. Gangopadhyay, B. Basu.- Reaction to extreme events in a minimal agent based model by A. Zaccaria, M. Cristelli, L. Pietronero.- Predatory trading and risk minimisation: how to (b)eat the competition by A. Mehta.- Statistical Mechanics of Labor Markets by He Chen, Jun-ichi Inoue.- Kolkata Paise Restaurant Problem: An Introduction by A. Ghosh, S. Biswas, A. Chatterjee, A.S. Chakrabarti, T. Naskar, M. Mitra, B.K. Chakrabarti.- Kolkata Paise Restaurant problem and the Cyclically Fair Norm by P. Banerjee, M. Mitra, C. Mukherjee.- An introduction to multi-player, multi-choice quantum games: Quantum Minority games & Kolkata restaurant problems by P. Sharif, H. Heydari.- Cluster analysis and Gaussian mixture estimation of correlated time-series by means of multi-dimensional scaling by T. Ibuki, Sei Suzuki. Jun-ichi Inoue.- Analyzing Crisis in Global Financial Indices by S. Kumar, N. Deo.- Study of Systemic Risk Involved in Mutual Funds by K.C. Dash, M. Dash.- Characterizing price index behavior through fluctuation dynamics by P.K. Panigrahi, S. Ghosh, A. Banerjee, J. Bahadur, P. Manimaran.- Discussions and comments.
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Do extreme price changes of pharmaceutical stocks reflect unexpected scientific information produced during the drug R&D process, especially the approval of new drugs, but also pre- and clinical trial results, recalls and withdrawals? Do stock prices initially overreact to such information? We modelled market-adjusted daily changes in stock prices of the 17 biggest pharmaceutical firms worldwide for the period from 1989 to 2008 to detect large price changes (outliers), using an Autoregressive Moving Average–Generalized Autoregressive Conditional Heteroscedasticity (ARMA–GARCH) dynamic econometric model. Then, we matched those outliers with news produced during the drug R&D process, and tested the hypothesis of no overreaction by examining cumulative abnormal returns. Our results show that there were 261 abnormal market-adjusted daily returns. In 60% of the cases, we were able to assign a plausible cause; i.e. Food and Drug Administration (FDA) approvals in 6% of these cases, news of a scientific nature in another 25%. Only 10 of 1721 FDA approvals of new drugs during the study period were related to abnormally large returns. The impact of negative news items on stock prices is larger than of positive news items. The overreaction hypothesis is rejected; there is no price backlash, therefore, the efficient market hypothesis is not violated.